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$\mathrm{Spin}^c$–structures and homotopy equivalences

Robert E Gompf

Geometry & Topology 1 (1997) 41–50

arXiv: math.GT/9705218

Abstract

We show that a homotopy equivalence between manifolds induces a correspondence between their spinc–structures, even in the presence of 2–torsion. This is proved by generalizing spinc–structures to Poincaré complexes. A procedure is given for explicitly computing the correspondence under reasonable hypotheses.

Keywords
4–manifold, Seiberg–Witten invariant, Poincaré complex
Mathematical Subject Classification
Primary: 57N13, 57R15
Secondary: 57P10, 57R19
References
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Publication
Received: 16 May 1997
Accepted: 17 October 1997
Published: 23 October 1997
Proposed: Ronald Stern
Seconded: Robion Kirby, Dieter Kotschick
Authors
Robert E Gompf
Department of Mathematics
The University of Texas at Austin
Austin
Texas 78712-1082
USA